arXiv subjects

Wendong Wang

Publications and source records attributed to Wendong Wang.

At least 19 recordsLinked to original sources

arXiv2026

Momentum-space engineering in van der Waals heterostructures

Twenty years of graphene research have established Dirac fermions as a versatile platform for exploring quantum topological phenomena. Yet control over graphene's low-energy spectrum mostly follows the route of miniband engineering using real-space superlattices. Here we introduce a complementary approach based on momentum-space 'Umklapp' band engineering. This is realised by matching reciprocal space positions of band edges of two adjacent highly incommensurate 2D crystals to coincide upon a boost from their Bragg vectors, creating resonant interlayer hybridisation that qualitatively reconstructs their spectra. To demonstrate this approach experimentally, we use monolayer graphene on MoS$_2$, twisted such that MoS$_2$ Q-valley states are brought by Umklapp into energy-momentum resonance with graphene's Dirac cones. The ensuing hybridization results in the formation of a clear additional Dirac-like spectral feature, identified by a distinct Landau-level fan and Shubnikov-de Haas oscillations characteristic to Berry phase $π$ electrons. These new topological spectral features create a spin-valley locked Ising system which is robust against small twist-angle variations that can be further tuned by an external displacement field. More broadly, Umklapp band engineering offers a practical strategy for tailoring the electronic structure in van der Waals heterostructures, expanding the design space of quantum materials beyond moiré superlattices and weak proximity effects.

cond-mat.mes-hall↗

arXiv2026

SSFMamba: Learning Symmetry-driven Spatial-Frequency Modeling for Physically Consistent 3D Medical Image Segmentation

Accurate 3D medical image segmentation requires a delicate balance between fine-grained local details and global contextual understanding. While spatial-domain models often struggle with long-range dependencies, existing frequency-based approaches frequently overlook intrinsic spectral properties such as Hermitian symmetry, leading to suboptimal feature integration. In this paper, we propose SSFMamba, a Mamba-based Symmetry-driven Spatial-Frequency fusion framework tailored for 3D medical imaging. Our architecture employs a complementary dual-branch design: the spatial branch models voxel sequences to preserve intricate anatomical textures, while the frequency branch operates on spectral components, each of which aggregates information from the entire volume, to capture global context. A core innovation is the 3D Multi-Directional Scanning Mechanism (MDSM), which integrates Hermitian symmetry with the causal nature of State Space Models (SSMs) to enable direction-aware global modeling. Crucially, by shifting the modeling focus to frequency-domain spectral components, SSFMamba captures the underlying structural characteristics of anatomical tissues. This leads to a highly adaptable framework that excels in both MRI and CT applications, regardless of the significant variations in intensity distributions. Extensive evaluations on the BraTS2020, BraTS2023, and BTCV datasets demonstrate that SSFMamba consistently outperforms state-of-the-art methods. Notably, our approach achieves exceptional performance on low-contrast organs such as the pancreas (81.97% Dice), underscoring its potential as a unified and physically consistent perception framework for diverse 3D clinical applications.

cs.CV↗

arXiv2026

Blow-up suppression for the 2D parabolic-parabolic Patlak-Keller-Segel-Navier-Stokes system

Chemotactic aggregation can overcome diffusion and lead to finite-time blow-up in Patlak-Keller-Segel models. Mixing induced by suitable fluid flows can counteract this aggregation through enhanced dissipation. Earlier results of Zeng-Zhang-Zi (J. Funct. Anal., 2021) for the coupled system impose additional smallness assumptions on the initial chemical gradient. A natural question is whether this restriction can be removed for the coupled system near a stationary Couette flow. We give a positive answer to this question for the two-dimensional parabolic-parabolic Patlak-Keller-Segel-Navier-Stokes system near the Couette flow $(Ay,0)$ in $\mathbb T\times\mathbb R$. It is proved that, when the Couette flow is strong enough ($A$ is large enough), the system admits a global solution that remains uniformly bounded in time for arbitrary fixed initial data. The main difficulties are the transient growth of the chemical gradient and the nonlinear coupling among the density, chemical field and fluid. We develop a two-stage energy method combining short-time estimates in Kelvin coordinates with long-time estimates in physical coordinates. The key is to split the nonzero chemical modes into two parts while accounting for the nonlinear transport. One part carries the initial data, and the other is a forced component with zero initial data. A weighted coupled energy controls the former through a time-integrable Gronwall coefficient and absorbs the feedback from the latter without increasing the initial energy. Enhanced dissipation then provides the bounds needed to enter the long-time regime, while one-dimensional zero-mode estimates and Moser iteration complete the argument without a mass restriction.

math.AP↗

arXiv2026

ClueTracer: Question-to-Vision Clue Tracing for Training-Free Hallucination Suppression in Multimodal Reasoning

Large multimodal reasoning models solve challenging visual problems via explicit long-chain inference: they gather visual clues from images and decode clues into textual tokens. Yet this capability also increases hallucinations, where the model generates content that is not supported by the input image or the question. To understand this failure mode, we identify \emph{reasoning drift}: during clue gathering, the model over-focuses on question-irrelevant entities, diluting focus on task-relevant cues and gradually decoupling the reasoning trace from visual grounding. As a consequence, many inference-time localization or intervention methods developed for non-reasoning models fail to pinpoint the true clues in reasoning settings. Motivated by these insights, we introduce ClueRecall, a metric for assessing visual clue retrieval, and present ClueTracer, a training-free, parameter-free, and architecture-agnostic plugin for hallucination suppression. ClueTracer starts from the question and traces how key clues propagate along the model's reasoning pathway (question $\rightarrow$ outputs $\rightarrow$ visual tokens), thereby localizing task-relevant patches while suppressing spurious attention to irrelevant regions. Remarkably, \textbf{without any additional training}, ClueTracer improves all \textbf{reasoning} architectures (including \texttt{R1-OneVision}, \texttt{Ocean-R1}, \texttt{MM-Eureka}, \emph{etc}.) by $\mathbf{1.21\times}$ on reasoning benchmarks

cs.CV↗

arXiv2026

PRISM: Prior Relational Information for Self-supervised Modeling to Enhance Solubility OOD Generalization

Solubility depends on intermolecular interactions between solutes and solvents, and is central to drug discovery, chemical and materials process engineering. Its prediction requires out-of-distribution (OOD) generalization to unseen solutes, solvents, and solvent mixtures, where supervised methods suffer from data scarcity, and existing self-supervised methods do not explicitly learn chemically meaningful relations. Learning chemically meaningful relational information without labels can alleviate data scarcity and improve OOD generalization, but remains challenging. We introduce Prior Relational Information for Self-supervised Modeling (PRISM) and apply it to solubility OOD generalization. PRISM is a label-free pretraining framework that converts expert-defined chemical priors into relational teachers. For solubility prediction, it trains four encoders to preserve the population-level relational information from priors capturing hydrophobic, electrostatic, polarizability, and substructural effects, using Kullback-Leibler (KL) divergence to match distance-based neighborhood distributions during pretraining. Across scaffold, solute, and solvent OOD settings, PRISM matches or surpasses supervised and self-supervised baselines. Under mixed-solvent OOD, freezing the four PRISM encoders and training a lightweight fusion-and-composition head outperforms strong baselines and substantially reduces run-to-run variation. Ablations and control studies confirm that gains stem from chemically meaningful relational structures baked into the encoders by PRISM. We expect this strategy of turning relational priors into self-supervision signals to extend beyond solubility prediction to domains where chemically or biologically meaningful relational priors are available.

cs.LG↗

arXiv2026

Suppression of blow-up in the 3D Patlak-Keller-Segel-Navier-Stokes system via non-parallel shear flows

In this paper, we consider the three-dimensional Patlak-Keller-Segel system coupled with the Navier-Stokes equations near the non-parallel shear flow $( Ay, 0, Ay )$ in $\mathbb{T}\times\mathbb{R}\times\mathbb{T}$. We show that if the shear flow is sufficiently strong (A is large enough), then the solutions to Patlak-Keller-Segel-Navier-Stokes system are global in time without any smallness restriction on the initial cell mass as long as the initial velocity satisfies $A^{\frac{2}{3}}\|u_{\rm in}\|_{H^2}\leq C_0$, which seems to be the first result of studying the suppression effect of shear flows for the 3D Patlak-Keller-Segel-Navier-Stokes system. Moreover, it implies that the solutions of the 3D Navier-Stokes equations are global in time if the initial velocity satisfies $A^{\frac{2}{3}}\|v_{\rm in}-(Ay,0,Ay)\|_{H^2}\leq C_0,$ which also shows the transition threshold for the shear flow $(Ay,0,Ay)$ in $\mathbb{T}\times\mathbb{R}\times\mathbb{T}$.

math.AP↗

arXiv2026

Global Regularity for the Chemotaxis-Stokes System with Signal Consumption in $\mathbb{R}^3$

In 2005, Tuval et al. introduced a continuum model for the interaction of aerobic bacteria, oxygen, and an incompressible fluid. For the associated three-dimensional chemotaxis-consumption systems, global classical regularity for large data has remained a longstanding question, even after omitting the nonlinear convection term from the fluid equation. We answer this question and prove global classical solvability of the chemotaxis--Stokes Cauchy problem in $\mathbb{R}^3$, with linear cell diffusion and bilinear signal consumption, under the following data assumptions. The initial density and signal are smooth, bounded, and nonnegative, with finite density mass and second moment and finite signal Fisher energy; the divergence-free initial velocity belongs to $H^4$. No smallness assumption is imposed, and a positive constant signal background is allowed. The solution remains bounded on every finite time interval. The main new ingredient is a localized entropy estimate uniform under density normalization, even when the resulting consumption coefficient becomes arbitrarily large. A terminal representation of the signal separates two complementary mechanisms: consumption excludes normalized density concentration at positive-signal points, while a localized weighted estimate improves density integrability at zero-signal points. Together, these mechanisms yield decay of a scale-invariant density quantity and allow a local $\varepsilon$-regularity criterion to be applied without a separate smallness assumption on the signal gradient.

math.AP↗

arXiv2026

On the sharp critical mass threshold for the 3D Patlak--Keller--Segel--Navier--Stokes system via Couette flow

As is well-known, the solution of the Patlak--Keller--Segel system in 3D may blow up in finite time regardless of any initial cell mass. In this paper, we are interested in the suppression of blow-up and the critical mass threshold for the 3D Patlak--Keller--Segel--Navier--Stokes system via the Couette flow $(Ay, 0, 0)$. It is proved that if the Couette flow is sufficiently strong ($A$ is large enough), the initial cell mass is less than $16π^{2}$, and the zero modes of the initial velocity are sufficiently small, then the solutions for the system are global in time. The threshold $16π^2$ seems to be optimal: for every finite $A>0$ and every $M>16π^2$, we show that there exist smooth positive initial densities of mass $M$, with zero initial velocity perturbation, whose corresponding solutions blow up in finite time. A key ingredient is a time-integrable decay estimate for the nonconstant part of the zero-mode velocity, which allows the logarithmic Hardy--Littlewood--Sobolev inequality to be used throughout the range $\frac{M}{2π}<8π$. Moreover, the global existence is obtained by combining quasi-linear space-time estimates proposed by Wei--Zhang (Comm. Pure Appl. Math., 2021) and a free-energy argument as in Bedrossian--He (SIAM J. Math. Anal., 2017) for the zero mode. The blow-up result follows from an exact invariant zero-mode reduction to the two-dimensional Patlak--Keller--Segel system and a localized virial argument.

math.AP↗

arXiv2026

Regular Solutions of the Stationary Navier-Stokes Equations in Arbitrarily High Dimensions

Recently, the existence of regular solutions $(u,p)$ to the stationary incompressible Navier--Stokes equations on $\mathbb R^n$ with bounded compactly supported forces $f$ for $5\le n\le15$ was established by Li--Yang (Comm. Math. Phys., 2022). However, it is still unknown whether there exists a regular solution for dimensions $n>15$. Here we answer this question and obtain the existence of regular solutions to the stationary Navier--Stokes equations in arbitrarily high dimensions. The key innovation is to combine an averaged signed pressure-potential identity with $L^2$-BMO estimates for the Bernoulli source flux, yielding a Bernoulli supremum bound independent of the size of the skew coefficient representing the drift. Together with the energy estimate for the comparison solution, this yields a sublinear bound for the Newtonian potential of the positive Bernoulli function, removing the upper dimension restriction in the earlier existence argument. We also construct periodic solutions and whole-space solutions for forces in $L^\infty\cap L^{2n/(n+2)}$. For compactly supported forces, we record two far-field profiles, their velocity, gradient and pressure remainders, and the corresponding cancellation criteria.

math.AP↗

arXiv2026

Robust low-rank tensor completion via factorized weighted tensor schatten-p norm minimization

Low-rank tensor factorization provides a flexible framework for completing multidimensional data from incomplete and corrupted observations. However, unweighted spectral regularizers impose a common shrinkage profile across singular components, which may excessively attenuate dominant low-rank components, and factorized variants either lack component-specific weighting or require costly singular value decompositions (SVDs). This paper proposes two weighted Schatten-$p$ tensor factorization models, termed \WSpTFI{} and \WSpTFII{}, under the tensor-tensor product (t-product) framework to address these limitations. \WSpTFI{} is motivated by a factorized weighted tensor Schatten-$p$ norm identity and permits flexible, possibly asymmetric factor exponents. \WSpTFII{} constructs a regularizer from transform-domain column-pair energies, yielding SVD-free main factor updates and a column-pruning mechanism for reducing redundant rank components. This paper further develops an iteratively reweighted alternating direction method of multipliers (ADMM)-type scheme for \WSpTFI{} and an iteratively reweighted least squares (IRLS)--block successive upper-bound minimization (BSUM) scheme for \WSpTFII{}. Theoretical analysis establishes the weighted factorization relation and provides a conditional limiting Karush--Kuhn--Tucker (KKT) characterization for \WSpTFI{}. For \WSpTFII{}, the actual damped quadratic block updates yield a quantitative sufficient-decrease mechanism for the fixed-$δ$ smoothed factor objective. This implies asymptotic regularity, and every accumulation point of the fixed-dimensional tail is stationary. Experiments on synthetic tensor completion, color-image restoration, hyperspectral inpainting, and printed-circuit-board defect detection demonstrate competitive reconstruction quality and robustness under various degradation conditions.

cs.CV↗

arXiv2026

A Critical Chemin--Lerner Regularity Criterion via One Velocity Component for the Three-Dimensional Navier--Stokes Equations

We prove a scaling-critical regularity criterion involving only one velocity component for finite-energy suitable weak solutions of the three-dimensional incompressible Navier--Stokes equations. Let $2<p<\infty$ and $m=3p/(p-2)$, so that $2/p+3/m=1$. We show that a singularity cannot occur provided \[ \sum_{j\in\mathbb Z} \|\dotΔ_j u^3\|_{L^p(0,T;L^m(\mathbb R^3))}<\infty, \] that is, $u^3\in\widetilde L^p(0,T;\dot B^0_{m,1}(\mathbb R^3))$. The assumption is a spatial-frequency $\ell^1$ refinement of the still unresolved critical condition $u^3\in L^p_tL^m_x$ and is complementary to the Lorentz-in-time refinement $L^{p,1}_tL^m_x$ obtained by Wang, Wu, and Zhang. By Bernstein embedding, the result extends to $u^3\in\widetilde L^p_t\dot B^s_{q,1}$ on the nonnegative-smoothness critical line $s=-1+2/p+3/q\ge0$. The principal innovation is a frequency--scale matching scheme embedded in the local energy inequality. Each dyadic block of $u^3$ is retained until it is paired with the vertical scale selected by a one-dimensional backward heat kernel. Low frequencies gain from the slab thickness, high frequencies from transferring the projection to the localized flux and applying an inverse Bernstein estimate, and spatially separated pressure sources from harmonic decay. These mechanisms generate a two-sided $\ell^1$ kernel, converting spatial-frequency summability into summability of physical-scale energy increments. Consequently, we obtain a uniform Type-I local energy bound without a Lorentz refinement in time; compactness and one-component rigidity then exclude singular blow-up limits whose third velocity component vanishes.

math.AP↗

arXiv2026

Moiré-induced lattice reconstruction at buried atomic interfaces

Atomic reconstruction at twisted two-dimensional interfaces governs many of their emergent optical, electronic, and mechanical properties, including sliding ferroelectricity. Despite recent progress in understanding lattice reconstruction in suspended twisted bilayers, structural changes at van der Waals heterointerfaces between multilayer crystals remain largely unexplored. Here we use multi-slice electron ptychography to non-invasively recover the three-dimensional atomic structure at marginally twisted rhombohedral interfaces between thick transition-metal dichalcogenide crystals. With a position precision of ~3 pm and a depth resolution ~1 nm, we resolve the twist-induced lattice reconstruction field per layer, and the resulting dislocation network at the buried interface. Despite the bulk nature, we observe markedly strong in-plane interfacial reconstruction due to suppression of the out-of-plane bending by outer layers, exceeding predictions from our three-dimensional modelling. Furthermore, we extract the strain tensor evolution during the decay of the reconstruction into the bulk, providing a structural foundation for understanding multi-layer moiré systems.

cond-mat.mes-hall↗

arXiv2026

Critical Morrey Rigidity and Removable Singularities for Five-Dimensional Stationary Navier-Stokes Flows

We prove a critical Morrey rigidity theorem for the five-dimensional stationary Navier--Stokes equations. More precisely, every smooth solution on $\mathbb R^5\setminus\{0\}$ satisfying \[ \sup_{R>0}R^{-2}\int_{B_R}|u|^3\,dx<\infty \] is identically zero, up to an additive constant in the pressure. This replaces the pointwise Type-I control in the known higher-dimensional rigidity theory by a velocity-only, scale-invariant averaged condition that allows spatial concentration. The proof develops a weak head-pressure mechanism that does not rely on pointwise pressure estimates or classical normal traces. We reconstruct a canonical pressure from the velocity, derive a renormalized inequality for the positive head pressure, and introduce two monotone radial fluxes. Annular energy estimates, suitable-weak compactness, and blow-up and blow-down limits are then used to identify the endpoint fluxes and force rigidity. As an application, we obtain a removable-singularity criterion in dimension five: if a suitable weak solution is smooth away from one point and either its scale-invariant Dirichlet energy or its cubic velocity Morrey quantity remains bounded near that point, then the singularity is removable. Thus, within the isolated-singularity class, the smallness assumption in the classical stationary regularity criterion is replaced by boundedness. We also prove the corresponding velocity-only cubic Morrey rigidity theorem in dimension four by a different finite-energy argument.

math.AP↗

arXiv2026

Boundary layer analysis for the 2D chemotaxis-Navier-Stokes system with logarithmic sensitivity, Part I: Well-posedness

This is the first part of a two-part work concerning the boundary layer convergence for chemotaxis-Navier-Stokes system in a two-dimensional half-space. In this paper, we investigate the chemotacxis-Navier-Stokes system with the logarithmic singularity under Navier-slip boundary conditions. More precisely, we perform an exact asymptotic expansion for the chemotaxis Navier-Stokes system with viscous coefficient $\varepsilon>0$, and obtain partial boundary layer profiles, establishing the well-posedness of the corresponding boundary layer profiles. Specially, we also establish the local well-posedness of solutions to the supercritical chemotaxis Euler equation (with $\varepsilon=0$) by overcoming the difficulty from the disappearance of diffusion terms.

math.AP↗

arXiv2026

New decay estimates and Liouville type theorems for the 3D axisymmetric stationary Navier-Stokes equations

The Liouville problem for the three-dimensional stationary Navier--Stokes equations remains open, even for axisymmetric $D$-solutions. In this paper, we obtain two results based on decay in the cylindrical radial variable $r=|x'|$. (i). Using a new pointwise Calderón--Zygmund estimate adapted to cylindrical geometry, we improve the decay estimates of Carrillo--Pan--Zhang (2020, JFA) and prove \[ |\nabla u_r|+|\nabla u_z| \lesssim r^{-5/4}[\log(\mathrm e+r)]^{5/4}, \quad |ω_r|+|ω_z| \lesssim r^{-9/8}[\log(\mathrm e+r)]^{9/8}, \quad r\gg1. \] (ii). We develop a new approach to Liouville theorems that improves the axisymmetric criteria of Wang (2019, JDE) and Zhao (2019, Nonlinear Anal.). Without any symmetry assumption, we show that a $D$-solution is trivial if one of the following holds: \[ (\mathrm a).\,\sup_{|x'|=r,\, z\in\mathbb R} |u(x',z)| \leq Cr^{-2/3}[\log(\mathrm e+r)]^{-γ}; \quad (\mathrm b).\, \sup_{|x'|=r,\, z\in\mathbb R} |ω(x',z)| \leq Cr^{-5/3}[\log(\mathrm e+r)]^{-γ}, \] for $r\geq1$, where $γ>1/3$.

math.AP↗

arXiv2026

Quantifying Influence and Information Transfer in a Modified Vicsek Model with Non-reciprocal Interactions

Understanding information transfer among individuals is fundamental to revealing the collective dynamics of complex systems. Information transfer has been quantified using various information-theoretic tools and assigned the concept of influence. However, information-theoretic measures are inherently statistical, not causal, and influence in the context of causal inference implies a causal relation, so equating influence with information transfer creates conceptual confusion and interpretational challenges. Here, we introduce an influence-based Vicsek model with non-reciprocal interactions to distinguish influence from information transfer and examine their relationship. At the pairwise level, for fixed noise strengths, influence and transfer entropy exhibit quasi-linear relations; for fixed interaction weights, influence and transfer entropy exhibit nonlinear relations. At the collective level, we find that both influence and normalized transfer entropy form two-branched relations that clearly identify the transition points across three distinct phase transitions. These transition points reveal a different aspect of the collective dynamics not captured by classical order parameters: phase transitions are associated with changes in the relative importance of influencers' presents or followers' presents on followers' futures. Finally, we use our model to assess partial information decomposition methods and identify two methods most suitable for analyzing our system, one based on pointwise surprisal changes and the other on secret key agreement. Our work is a first step in distinguishing the concept of influence from information transfer in a physical model system, provides a concrete testbed for methods emerging from the growing field of information theory-based causal inference, and offers new insights into the dynamics of complex systems.

cond-mat.stat-mech↗

arXiv2026

Global bounded solutions for a class of generalized Hillen-Painter models near Couette flow in $\mathbb{R}^2$

We investigate the global well-posedness of a class of generalized Hillen--Painter systems -- specifically, supercritical volume-filling chemotaxis models -- in $\mathbb{R}^2$ under the influence of Couette flow. It is well established that, in the absence of fluid flow, solutions to this system may develop finite-time singularities (blow-up) for arbitrary initial cell mass. It is proved that the introduction of a Couette flow with sufficiently large amplitude guarantees the global existence of solutions for all initial masses. By employing a novel frequency decomposition technique, we successfully remove the mass threshold limitation presented in previous studies on the domain $\mathbb{T}\times\mathbb{R}$ (Wang et al., Commun. Contemp. Math.), thereby establishing global regularity in the whole space without any smallness assumptions.

math.AP↗

arXiv2026

Critical mass threshold for the 2D Patlak-Keller-Segel-Navier-Stokes system

In this paper, we investigate critical mass threshold for the Patlak-Keller-Segel-Navier-Stokes system on the two-dimensional whole space and obtain global existence of strong solutions if the initial mass is less than or equal to $8π$, regardless of the initial norm of the velocity. One new observation is that the local mass of the density function rearrangement satisfies a good inequality that is independent of velocity; and then an improved maximum principle is applied by choosing a nice auxiliary function.

math.AP↗